Convolving Shell Sensors and Actuators Applied to Rings

Spillover problems can occur when modal cross couplings introduced by the residual modes come into feedback in a closed—loop distributed control system. Observation spillover is due to the infinite summation of feedback control forces in the closed—loop control equations, and this spillover can introduce unstable dynamic responses in undamped structural systems (Meirovitch & Baruh, 1983). Thus, it is highly desirable that sensors only monitor those modes needed to be controlled such that observation spillover is prevented. In reality, however, sensors not only respond to controlled modes, but also those uncontrolled residual modes. There are several techniques of reducing the observation spillover. Conventional practice is to place sensors, spatially discrete sensors, at modal nodes or nodal lines of the residual modes. The difficulty with this arrangement is that it is very difficult, if not impossible, to avoid all uncontrolled residual modes. Another common approach is to pre—filter the sensor data using a comb filter with phase—locked loops (Gustafson & Speyer, 1976). The phase—locked loop filter reduces the observation spillover in the frequency domain. This technique requires that 1) the controlled modal frequencies are precisely known; 2) there is a reasonable separation from the nearby residual modes; 3) the signal—to—noise ratio is sufficiently high. The other method is to use spatially distributed modal sensors which respond only to a structural mode or a group of modes. In addition, feedback control forces for controlled modes could also appear in the governing equations of other uncontrolled modes resulting from modal interactions among all participating modes — control spillover.